This is a proof-of-concept implementation of Clausen/Baum's FFT for the symmetric group.

For a thorough introduction to FFTs over the symmetric group, check out the following useful references:

• Fast Fourier Transforms for the Symmetric Group: Theory and Implementation, Michael Clausen and Ulrich Baum (1993)
• Efficient computation of the Fourier transform on finite groups, Persi Diaconis, Daniel Rockmore (1990)

• numpy
• python3 (nothing in here absolutely requires python3 but most of the printing uses string formatting which is slightly different in 3)